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Two different prime numbers between 4 and 18 are chosen. When their su 14 Mar 2019, 22:20
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

76% (02:09) correct 24% (02:17) wrong based on 161 sessions

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Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following number could be obtained?

(A) 21

(B) 60

(C) 119

(D) 180

(E) 231
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C
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Two different prime numbers between 4 and 18 are chosen. When their su 14 Mar 2019, 23:24
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TyrionLannister
Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following number could be obtained?

(A) 21

(B) 60

(C) 119

(D) 180

(E) 231
Show more

Prime numbers greater than 2 will be both odd. So their sum will be even since odd + odd = even and their product will be odd since odd*odd = odd
Product - Sum = odd - even = odd
So options (B) and (D) are out.

The greater the numbers, the greater the product though the sum will increase slowly. Hence Product - Sum will increase as the numbers increase. Let's find the max and min value of Product - Sum

Min: The prime numbers are 5 and 7
Product - Sum = 23

Max: The prime numbers are 13 and 17
Product - Sum = 221 - 30 = 191

The only value lying in this range is 119.

Answer (C)
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Two different prime numbers between 4 and 18 are chosen. When their su 15 Mar 2019, 00:33
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Prime numbers between 4 and 18 are 5,7,11,13,17

One thing to notice here is all the numbers are odd.
Therefore
Product = Odd x Odd=Odd
Sum = Odd + Odd = Even

Difference = Odd - Even = Odd
There B and D are eliminated

E is eliminated because no product is greater than or equal to 231

Now option C 119 = 143 (13x11) - 24(13+11) Hence the correct answer
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Two different prime numbers between 4 and 18 are chosen. When their su 15 Mar 2019, 01:25
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Solution



Given:
    • Two different prime numbers between 4 and 18 are chosen.

To find:
    • Among the given options, which one can be the result when their sum is subtracted from their product.

Approach and Working:
Between 4 and 18, the prime numbers are: 5, 7, 11, 13 and 17.
Let us take 2 distinct primes from the given list and subtract their sum from their product.
    • For 5 and 7: (5 x 7) – (5 + 7) = 35 – 12 = 23
    • For 5 and 11: (5 x 11) – (5 + 11) = 55 – 16 = 39
    • For 5 and 13: (5 x 13) – (5 + 13) = 65 – 18 = 47
    • For 5 and 17: (5 x 17) – (5 + 17) = 85 – 22 = 63
    • For 7 and 11: (7 x 11) – (7 + 11) = 77 – 18 = 59
    • For 7 and 13: (7 x 13) – (7 + 13) = 91 – 20 = 71
    • For 7 and 17: (7 x 17) – (7 + 17) = 119 – 24 = 95
    • For 11 and 13: (11 x 13) – (11 + 13) = 143 – 24 = 119

As 119 is given in the choices, it is the correct answer.

Hence, the correct answer is option C.

Answer: C

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Two different prime numbers between 4 and 18 are chosen. When their su 15 Mar 2019, 07:22
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Bunuel

TOUGH QUESTION:



Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?

(A) 21
(B) 60
(C) 119
(D) 180
(E) 231
Show more


Note:

5, 7 , 11 , 13 , 17 .

All are odd integers so when we are going to multiply any of the 2 integers we will get an odd result.

If we add 2 odd integers, we will get an even integers.

Odd - Even = Odd.

Thus, eliminate B and D.

Option E) 17 * 13 = 224. Thus , option is just an bogus option. greater 2 integers yield 224. thus answer can't be 231.

Option C) 119 is slightly large integer, Thus , don't take all the greater integers.

11* 13 = 143

11 + 13 = 24

143 - 24 = 119.

Thus , C is the correct answer.
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Two different prime numbers between 4 and 18 are chosen. When their su 07 Sep 2020, 00:33
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Noshad
Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following number could be obtained?

(A) 21

(B) 60

(C) 119

(D) 180

(E) 231
Show more

Min Prime Nos are - 5,7

Their sum is 12 & Product is 35

When their sum is subtracted from their product

\(35 - 12 = 23\)

Max Prime Nos are - 13,17

Their sum is 40 & Product is 221

When their sum is subtracted from their product

\(221 - 40 = 181\)

Thus the range will be between 23 to 181 (Options A and E can be rejected)


Now use the properties ...

Product of 2 Prime (Except 2 ) are always ODD
Sum of 2 Prime is always EVEN

Thus, ODD - EVEN = ODD , Hence correct answer must always be ODD, among the remaining options (B, C & D) only C is possible, Thus Answer must be (C)
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Two different prime numbers between 4 and 18 are chosen. When their su 19 Jun 2025, 00:19
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